A327484 Number of integer partitions of 2^n whose mean is a power of 2.

1, 2, 4, 11, 66, 1417, 178803, 275379307, 15254411521973, 108800468645440803267, 964567296140908420613296779144, 219614169629364529542990295052656098001967511, 38626966436500261962963100479469496821891576834974275502742922521

Offset: 0

Author

Gus Wiseman, Sep 13 2019

Keywords

• nonn

Comments

Number of partitions of 2^n whose number of parts is a power of 2. - Chai Wah Wu, Sep 21 2023

Examples

			The a(0) = 1 through a(3) = 11 partitions:
  (1)  (2)   (4)     (8)
       (11)  (22)    (44)
             (31)    (53)
             (1111)  (62)
                     (71)
                     (2222)
                     (3221)
                     (3311)
                     (4211)
                     (5111)
                     (11111111)
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..15 (n = 0..13 from Alois P. Heinz)

Crossrefs

Row sums of A327483.

Cf. A067538, A068413, A135342, A237984, A327474, A327481, A327482.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[2^n],IntegerQ[Mean[#]]&]],{n,0,5}]

Python

from sympy.utilities.iterables import partitions
def A327484(n): return sum(1 for s,p in partitions(1<Chai Wah Wu, Sep 21 2023

Python

# uses A008284_T
def A327484(n): return sum(A008284_T(1<Chai Wah Wu, Sep 21 2023

Extensions

a(7) from Chai Wah Wu, Sep 14 2019

a(8)-a(11) from Alois P. Heinz, Sep 21 2023

a(12) from Chai Wah Wu, Sep 21 2023